XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #361,551

Block #361,551

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/16/2014, 3:46:28 AM Β· Difficulty 10.4060 Β· 6,451,033 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
2cce3f97efd947a55e4007a92b5878ea3cebbd4aa25ad911eb2e011f7d12fe2f
View on Chainz β†—

Height

#361,551

Difficulty

10.406022

Transactions

1

Size

190 B

Version

2

Bits

0a67f108

Nonce

355,164

Timestamp

1/16/2014, 3:46:28 AM

Confirmations

6,451,033

Merkle Root

f0a27abf286131256901788613feff32924fe1ab0df965c142d9bdc25e33728b
Transactions (1)
Coinbasef0a27abf286131…d9bdc25e33728b
1 in β†’ 1 out9.2200 XPM97 B
AWQBKr3Y…sUA1Ehpd
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.136 Γ— 10¹⁰²(103-digit number)
41363886443850773333…91811492439985738960
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
4.136 Γ— 10¹⁰²(103-digit number)
41363886443850773333…91811492439985738959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.272 Γ— 10¹⁰²(103-digit number)
82727772887701546666…83622984879971477919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.654 Γ— 10¹⁰³(104-digit number)
16545554577540309333…67245969759942955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.309 Γ— 10¹⁰³(104-digit number)
33091109155080618666…34491939519885911679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.618 Γ— 10¹⁰³(104-digit number)
66182218310161237332…68983879039771823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.323 Γ— 10¹⁰⁴(105-digit number)
13236443662032247466…37967758079543646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.647 Γ— 10¹⁰⁴(105-digit number)
26472887324064494933…75935516159087293439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.294 Γ— 10¹⁰⁴(105-digit number)
52945774648128989866…51871032318174586879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.058 Γ— 10¹⁰⁡(106-digit number)
10589154929625797973…03742064636349173759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.117 Γ— 10¹⁰⁡(106-digit number)
21178309859251595946…07484129272698347519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 361551

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 2cce3f97efd947a55e4007a92b5878ea3cebbd4aa25ad911eb2e011f7d12fe2f

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #361,551 on Chainz β†—
Circulating Supply:57,744,707 XPMΒ·at block #6,812,583 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy